Divide the polynomials.
Answer: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice the numerator is missing a $1^{\text{st}}$ degree term. Let's add it as $0x$. $\begin{array}{r} x-3 \\ x+3|\overline{x^2+0x-7} \\ \mathllap{-(}\underline{x^2+3x\phantom{+7}\rlap )} \\ -3x-7 \\ \mathllap{-(}\underline{-3x-9\rlap )} \\ 2 \end{array}$ We get that the quotient is $x-3$ and the remainder is $2$, and therefore: $\dfrac{x^2-7}{x+3}=x-3+\dfrac{2}{x+3}$ [I want to see a different way of performing the division.]